Use square root and cube root symbols to represent solutions to equations of the form x<sup>2</sup> = p and x<sup>3</sup> = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that â2 is irrational.

Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. For example, estimate the population of the United States as 3 Ã 10<sup>8</sup> and the population of the world as 7 Ã 10<sup>9</sup>, and determine that the world population is more than 20 times larger.

Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology.

Start Up

Today's lesson offers students a chance to self-assess their understanding. The lesson employs a Digital_Worksheet to allow students independence, provide challenging tasks, and embed learning resources. Through the worksheet, I offer students a series of practice questions online. I have also planned follow up questions for the end of the lesson to assess student progress.

The learning supports provided on the Digital Worksheet include video help as well as answers. As students work I circulate and intervene with 1-on-1 support. I encourage students to take notes as they work, and, to ask questions when they need help. I motivate students by saying, "I want you to use this time to be ready for whatever questions I ask on today's for an Exit Ticket."

Digital_Worksheet.png

The Digital Worksheet

35 minutes

Since many of questions are more basic scientific notation questions, I tend to use this assessment early in my scientific notation unit. However, from year to year, this may change and I might choose to use it closer to a summative assessment, perhaps as a warm up.

Before beginning, I ask students to get their pen or pencil and a piece of paper out. As they do this I hand out laptop computers so students can access the worksheet electronically. If any students require a printed copy (for whatever reason), I print out the worksheet for them.

Submit your answers online (I create self grading Google Forms so the students can see how they did)

Create a question that is based on but slightly more difficult than a question from this worksheet.

The Digital Worksheet - Scientific Notation.pdf

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Review

10 minutes

During I lesson like this, I also plan some time to review how the assessment went. I structure the time to go deeper than right and wrong answers. I introduce it to students as a time to share their ideas. I say something like, "What ideas did you have as you worked on these problems? What observations? What did you discover? Remember?"

For example, consider the Temperature_of_the_Sun_Problem. The temperature of the sun is stated to be 27 million degrees. I want students to recognize why the answer is 2.7 x 10^7 and not 27 x 10^6. I also want them to recognize that these two expressions are equal. I would also ask them to be able to extend this idea to other equivalent numerical expressions.

.27 x 10^8

.027 x 10^9

.0027 x 10^10

and so forth...

Ultimately, my idea is to use each question as an opportunity for reflection, and to promote meaningful reflection as a mathematical practice (MP3).

Temperature_of_the_Sun_Problem.png

Exit Ticket

10 minutes

For this lesson's Exit Ticket, I ask students to create a question that is slightly more difficult, but based upon, one of the questions from the worksheet. After students write their questions, I pick 5 that I like and show them to the class. I give students about 1-2 minutes to answer each question. I collect the students answers to these 5 questions at the end of class.

Teaching Note: I highly recommend giving this idea a shot. Student created questions are always fun to read and will make the members of your class a contributing member of the assessment process.